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It appears that you are conflating a field gradient with a potential energy gradient.

Potential energy changes when moving parallel to any field force, regardless of whether that field is static or has some gradient.

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Let us consider an experiment. Take a long cylindrical coil, so that in most of the coil the magnetic field is constant. In the center, place a diamagnetic material. Does it experience a force toward either end of the coil? If not, why not, according to your reasoning? If so, why does it experience a force toward that end of the coil and not the other?

I misinterpreted your point due to my own misunderstanding of quantum spin, a subject I'm currently studying. I see your point now, due to the dipole nature of magnetism, and the confusion came from the original "so you could not do the same for a human," in which I think you meant "you could not do the same in a perfectly uniform field."

This back and forth was fantastic to read, though I understand basically none of it.

You could not do it to a human because you'd need a nonuniform field over a much larger distance, which means the maximum of that field would have to be enormous, far higher than in the frog case, and far higher than could be generated by any practical electromagnet, superconducting or otherwise.

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